Theory of the many-body localization transition in one dimensional systems

By Ronen Vosk, D. Huse, E. Altman. 2014

307 citations recorded by the source corpus.

We formulate a theory of the many-body localization transition based on a novel real space renormalization group (RG) approach. The results of this theory are corroborated and intuitively explained with a phenomenological effective description of the critical point and of the "badly conducting" state found near the critical point on the delocalized side. The theory leads to the following sharp predictions: (i) The delocalized state established near the transition is a Griffiths phase, which exhibits sub-diffusive transport of conserved quantities and sub-ballistic spreading of entanglement. The anomalous diffusion exponent $\alpha < 1/2$ vanishes continuously at the critical point. The system does thermalize in this Griffiths phase. (ii) The many-body localization transition is controlled by a new kind of infinite randomness RG fixed point, where the broadly distributed scaling variable is closely related to the eigenstate entanglement entropy. Dynamically, the entanglement grows as $\sim\log t$ at the critical point, as it also does in the localized phase. (iii) In the vicinity of the critical point the ratio of the entanglement entropy to the thermal entropy, and its variance (and in fact all moments) are scaling functions of $L/\xi$, where $L$ is the length of the system and $\xi$ is the correlation length, which has a power-law divergence at the critical point.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/21f6ebf920a0252bd66f1a4ef4f73c5486f66ac9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. V. Khemani
2. D. Abanin
3. D. Huse
4. Tomaz Prosen
5. Maksym Serbyn
6. J. Imbrie
7. Romain Vasseur
8. J. Moore

In Statistical and Nonlinear Physics

1. V. Khemani
2. Tomaz Prosen
3. J. Moore
4. Romain Vasseur
5. D. Huse
6. L. Vidmar
7. S. Gopalakrishnan
8. J. Bonvca

Citations in the corpus

• Criterion for Many-Body Localization-Delocalization Phase Transition (2015, unknown): “Such dynamics at the MBL transition was predicted by recent phenomenological RG studies of the MBL transition [28, 29].”
• Ergodicity breaking transition in finite disordered spin chains (2020, methodology): “MBL and the corresponding transition were widely studied by means of numerical approaches [35, 45–73] and phenomenological theories [74–85], as well as experimentally [86–92].”
• Colloquium : Many-body localization, thermalization, and entanglement (2018, background): “Different RG schemes were proposed to describe this process (Dumitrescu et al., 2017; Goremykina et al., 2018; Potter et al., 2015; Thiery et al., 2017; Vosk et al., 2015; Zhang et al., 2016).”
• Observation of many-body localization of interacting fermions in a quasirandom optical lattice (2015, background): “In contrast to x, however, x* is expected to remain finite at the transition (48).”
• Probing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasiperiodic Systems (2017, background): “Extrapolating from one-dimension, where vanishing of this relaxation exponent at a critical disorder strength ∆c signals a transition into an MBL phase [19, 20, 23, 26, 33, 35], our observations would support a transition into an MBL phase in two dimensions in the isolated limit.”
• Spectral statistics across the many-body localization transition (2015, background): “deed the strong overlaps only between adjacent energy levels imply logarithmic transport [20], predicted at the MBLT [14, 15].”
• Local integrals of motion in many‐body localized systems (2016, background): “1 As opposed to the linear growth in clean integrable or non-integrable systems [22, 60] and to the sub-ballistic growth in disordered, delocalized systems close to the MBL phase [67, 103].”
• Critical Properties of the Many-Body Localization Transition (2016, background): “At these fixed points, the fraction of the sample that is in the entangled clusters is very small: about 1% or less [22,23].”
• Avalanches and many-body resonances in many-body localized systems (2021, methodology): “We should therefore provide some clarification on how we use the term “many-body resonance”, which has been used variously to describe many physical scenarios ranging from resonances between thermal blocks in phenomenological RGs to isolated “Mott-like” resonances in manybody eigenstates [19, 20, 54”